Narrowing region for tropical convections in the western North Pacific

Considering that the subtropical highs and tropical convections are observed as negative and positive vorticities respectively, the large-scale features of the atmospheric environment can be effectively represented using streamfunctions as defined by the Laplacian. By investigating the geographical patterns of streamfunctions from different modes of environmental variability, this study conceptualizes how the subtropical high expands and the region for tropical convections migrates in the western North Pacific. It is confirmed that, owing to the expansion of the subtropical high, the limited ocean area for tropical convections even bounded by the equator becomes narrower in the “La Niña mode” than that in the “El Niño mode”. This study finds that a warmer environment is likely to further expand the subtropical high to the west, and then the westernmost shift in the region for tropical convections appears in the “warmer La Niña mode”. A linear perspective suggests that every warmer La Niña environment could be one that people have scarcely experienced before.


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. The same as in Supplementary Fig. 2, but for "Colder mode (C)", "Normal (N)", and "Warmer mode (W)" from top to bottom. Fig. 4. The same as in Supplementary Fig. 2, but for "Colder La Niña mode (CL)", "La Niña mode (L)", and "Warmer La Niña mode (WL)" from top to bottom. Supplementary Fig. 5 demonstrates the streamfunction for each mode of variability. The expansion of subtropical high between CE to LW is most apparent, and the geographical spectrum of the patterns is shown in Fig. 3b (main manuscript). Blue crosses demonstrate the significant area at 95% confidence level. It shows that significant areas differ by modes of variability. Here in (a) and (h), we find that CE and WL modes show significant response in most areas, which support the conclusion of the current study, that is "This study finds that a warmer environment is likely to further expand the subtropical high to the west, and then the westernmost shift in the region for tropical cyclone activity appears in the "warmer La Niña mode" (in main manuscript).

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Suppl. Fig. 5. Modeled streamfunction for each mode of variability, and the significant area at 95 % confidence level denoted by blue crosses. The black rectangles shown are the same as in Fig. 3 (main manuscript).

Density distribution of TC genesis longitude
Narrowing region for TC activity according to expanding subtropical highs is also examined by Supplementary Fig. 6. The results generally show the similar responses as vorticities in Fig.   4 (main manuscript), but the response looks poor in describing the patterns compared to the vorticities. The westward moving pattern appears mostly clear in (d). In (a), the pattern of WE slightly shows westward difference from CE, but not apparent. The patterns between C and W in (c) are not consistent with

Assigning the closest variability mode to annual observation
In a Cartesian space, each observation indicates the ENSO status and the level of global ocean warmth for JJASON per year (Supplementary Fig. 7). There are 36 observations  on an annual basis. The closest variability mode among the eight is assigned to each year.
While black color represents the events closest to ENSO modes, blue and orange around denote the events closest to the colder anomalies (CE, CL) and the warmer anomalies (WE, WL), respectively. The rest (C, W) are colored in green. Fig. 7. Observed ENSO status and global warmth level over the 36 years  during JJASON. Each circle indicates the closest mode of environmental variability by different colors. Cold and warm anomalies are denoted by blue and orange color, respectively. The rest (C, W) are colored in green. The last two digits of year number are displayed for each year.

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A two-dimensional continuous variability space can be organized using any two primary variables 1 . In the current study, the two variables of NSOI and GMSST are used for the primary variables. The primary variables indicate the time series of annual ENSO status and global warmth level, respectively. Though the two are independent, it doesn't mean they have an orthogonal relationship. Only the principal components are orthogonal meaning no correlation.
From the continuous variability space, any directional variability (DV) can be identified as the combination of ENSO status and global warmth level, implying varying weights on the two primary variables. DV can be defined by the angle (θ) starting from GMSST. Here, PC1 and PC2 are understood as special cases when equal weights are applied to the primary variables.
Equal weights mean θ = π/4. While PC1 is the directional variability where equal weights are given to NSOI and GMSST, while PC2 is the same as PC1 but with negative sign on NSOI.
This method attempts to show that the variabilities are continuously linked and so do the patterns by the modes of environmental variability.
Suppl. Fig. 8. A diagram of two-dimensional continuous variability space. The two variables of NSOI and GMSST are used for the primary variables. PC1 and PC2 represent the two principal components. DV denotes a directional variability depending on a counterclockwise angle (θ) starting from GMSST.